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Description of Statistical Computation

Author's title

Author*The author of this computation has been verified*
R Software Modulerwasp_smp.wasp
Title produced by softwareStandard Deviation-Mean Plot
Date of computationFri, 12 Dec 2008 06:29:54 -0700
Cite this page as followsStatistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?v=date/2008/Dec/12/t1229088653ugod97834075uk4.htm/, Retrieved Fri, 17 May 2024 14:49:47 +0000
Statistical Computations at FreeStatistics.org, Office for Research Development and Education, URL https://freestatistics.org/blog/index.php?pk=32709, Retrieved Fri, 17 May 2024 14:49:47 +0000
QR Codes:

Original text written by user:
IsPrivate?No (this computation is public)
User-defined keywords
Estimated Impact210

Tree of Dependent Computations

Family? (F = Feedback message, R = changed R code, M = changed R Module, P = changed Parameters, D = changed Data)
-     [Standard Deviation-Mean Plot] [WS7 Q1 G6 reeks 1] [2007-11-22 09:45:51] [22f18fc6a98517db16300404be421f9a]
- R  D  [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 13:19:31] [29747f79f5beb5b2516e1271770ecb47]
-    D      [Standard Deviation-Mean Plot] [Standard Deviatio...] [2008-12-12 13:29:54] [c0a347e3519123f7eef62b705326dad9] [Current]
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Dataset

Dataseries X:
Download CSV
Histogram
Boxplots 
15044.5
14944.2
16754.8
14254
15454.9
15644.8
14568.3
12520.2
14803
15873.2
14755.3
12875.1
14291.1
14205.3
15859.4
15258.9
15498.6
15106.5
15023.6
12083
15761.3
16943
15070.3
13659.6
14768.9
14725.1
15998.1
15370.6
14956.9
15469.7
15101.8
11703.7
16283.6
16726.5
14968.9
14861
14583.3
15305.8
17903.9
16379.4
15420.3
17870.5
15912.8
13866.5
17823.2
17872
17420.4
16704.4
15991.2
16583.6
19123.5
17838.7
17209.4
18586.5
16258.1
15141.6
19202.1
17746.5
19090.1
18040.3
17515.5
17751.8
21072.4
17170
19439.5
19795.4
17574.9
16165.4
19464.6
19932.1
19961.2
17343.4
18924.2
18574.1
21350.6
18594.6
19823.1
20844.4
19640.2
17735.4
19813.6
22160
20664.3
17877.4
21211.2
21423.1
21688.7
23243.2
21490.2
22925.8
23184.8
18562.2

Tables (Output of Computation)





Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132

\begin{tabular}{lllllllll}
\hline
Summary of computational transaction \tabularnewline
Raw Input & view raw input (R code)  \tabularnewline
Raw Output & view raw output of R engine  \tabularnewline
Computing time & 1 seconds \tabularnewline
R Server & 'George Udny Yule' @ 72.249.76.132 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32709&T=0

[TABLE]
[ROW][C]Summary of computational transaction[/C][/ROW]
[ROW][C]Raw Input[/C][C]view raw input (R code) [/C][/ROW]
[ROW][C]Raw Output[/C][C]view raw output of R engine [/C][/ROW]
[ROW][C]Computing time[/C][C]1 seconds[/C][/ROW]
[ROW][C]R Server[/C][C]'George Udny Yule' @ 72.249.76.132[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32709&T=0

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32709&T=0

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Summary of computational transaction
Raw Inputview raw input (R code)
Raw Outputview raw output of R engine
Computing time1 seconds
R Server'George Udny Yule' @ 72.249.76.132






Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114791.0251185.201388429984234.6
214896.71666666671233.528074510694860
315077.91240.852211550235022.8
416421.8751409.654893372524037.4
517567.63333333331347.030088975774060.5
618598.851511.140765057374907
719666.8251391.760931093484424.6

\begin{tabular}{lllllllll}
\hline
Standard Deviation-Mean Plot \tabularnewline
Section & Mean & Standard Deviation & Range \tabularnewline
1 & 14791.025 & 1185.20138842998 & 4234.6 \tabularnewline
2 & 14896.7166666667 & 1233.52807451069 & 4860 \tabularnewline
3 & 15077.9 & 1240.85221155023 & 5022.8 \tabularnewline
4 & 16421.875 & 1409.65489337252 & 4037.4 \tabularnewline
5 & 17567.6333333333 & 1347.03008897577 & 4060.5 \tabularnewline
6 & 18598.85 & 1511.14076505737 & 4907 \tabularnewline
7 & 19666.825 & 1391.76093109348 & 4424.6 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32709&T=1

[TABLE]
[ROW][C]Standard Deviation-Mean Plot[/C][/ROW]
[ROW][C]Section[/C][C]Mean[/C][C]Standard Deviation[/C][C]Range[/C][/ROW]
[ROW][C]1[/C][C]14791.025[/C][C]1185.20138842998[/C][C]4234.6[/C][/ROW]
[ROW][C]2[/C][C]14896.7166666667[/C][C]1233.52807451069[/C][C]4860[/C][/ROW]
[ROW][C]3[/C][C]15077.9[/C][C]1240.85221155023[/C][C]5022.8[/C][/ROW]
[ROW][C]4[/C][C]16421.875[/C][C]1409.65489337252[/C][C]4037.4[/C][/ROW]
[ROW][C]5[/C][C]17567.6333333333[/C][C]1347.03008897577[/C][C]4060.5[/C][/ROW]
[ROW][C]6[/C][C]18598.85[/C][C]1511.14076505737[/C][C]4907[/C][/ROW]
[ROW][C]7[/C][C]19666.825[/C][C]1391.76093109348[/C][C]4424.6[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32709&T=1

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32709&T=1

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Standard Deviation-Mean Plot
SectionMeanStandard DeviationRange
114791.0251185.201388429984234.6
214896.71666666671233.528074510694860
315077.91240.852211550235022.8
416421.8751409.654893372524037.4
517567.63333333331347.030088975774060.5
618598.851511.140765057374907
719666.8251391.760931093484424.6






Regression: S.E.(k) = alpha + beta * Mean(k)
alpha512.706537828823
beta0.04896754563291
S.D.0.0153703856375487
T-STAT3.18583715383731
p-value0.0243783117652102

\begin{tabular}{lllllllll}
\hline
Regression: S.E.(k) = alpha + beta * Mean(k) \tabularnewline
alpha & 512.706537828823 \tabularnewline
beta & 0.04896754563291 \tabularnewline
S.D. & 0.0153703856375487 \tabularnewline
T-STAT & 3.18583715383731 \tabularnewline
p-value & 0.0243783117652102 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32709&T=2

[TABLE]
[ROW][C]Regression: S.E.(k) = alpha + beta * Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]512.706537828823[/C][/ROW]
[ROW][C]beta[/C][C]0.04896754563291[/C][/ROW]
[ROW][C]S.D.[/C][C]0.0153703856375487[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.18583715383731[/C][/ROW]
[ROW][C]p-value[/C][C]0.0243783117652102[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32709&T=2

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32709&T=2

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: S.E.(k) = alpha + beta * Mean(k)
alpha512.706537828823
beta0.04896754563291
S.D.0.0153703856375487
T-STAT3.18583715383731
p-value0.0243783117652102






Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.00487122023594
beta0.636496426427227
S.D.0.184771483590712
T-STAT3.44477629371171
p-value0.0183406294559014
Lambda0.363503573572773

\begin{tabular}{lllllllll}
\hline
Regression: ln S.E.(k) = alpha + beta * ln Mean(k) \tabularnewline
alpha & 1.00487122023594 \tabularnewline
beta & 0.636496426427227 \tabularnewline
S.D. & 0.184771483590712 \tabularnewline
T-STAT & 3.44477629371171 \tabularnewline
p-value & 0.0183406294559014 \tabularnewline
Lambda & 0.363503573572773 \tabularnewline
\hline
\end{tabular}
%Source: https://freestatistics.org/blog/index.php?pk=32709&T=3

[TABLE]
[ROW][C]Regression: ln S.E.(k) = alpha + beta * ln Mean(k)[/C][/ROW]
[ROW][C]alpha[/C][C]1.00487122023594[/C][/ROW]
[ROW][C]beta[/C][C]0.636496426427227[/C][/ROW]
[ROW][C]S.D.[/C][C]0.184771483590712[/C][/ROW]
[ROW][C]T-STAT[/C][C]3.44477629371171[/C][/ROW]
[ROW][C]p-value[/C][C]0.0183406294559014[/C][/ROW]
[ROW][C]Lambda[/C][C]0.363503573572773[/C][/ROW]
[/TABLE]
Source: https://freestatistics.org/blog/index.php?pk=32709&T=3

Globally Unique Identifier (entire table): ba.freestatistics.org/blog/index.php?pk=32709&T=3

As an alternative you can also use a QR Code:  
QR Code


The GUIDs for individual cells are displayed in the table below:

Regression: ln S.E.(k) = alpha + beta * ln Mean(k)
alpha1.00487122023594
beta0.636496426427227
S.D.0.184771483590712
T-STAT3.44477629371171
p-value0.0183406294559014
Lambda0.363503573572773


Figures (Output of Computation)

Input Parameters & R Code

Parameters (Session):
par1 = 12 ;
Parameters (R input):
par1 = 12 ;
R code (references can be found in the software module):
par1 <- as.numeric(par1)
(n <- length(x))
(np <- floor(n / par1))
arr <- array(NA,dim=c(par1,np))
j <- 0
k <- 1
for (i in 1:(np*par1))
{
j = j + 1
arr[j,k] <- x[i]
if (j == par1) {
j = 0
k=k+1
}
}
arr
arr.mean <- array(NA,dim=np)
arr.sd <- array(NA,dim=np)
arr.range <- array(NA,dim=np)
for (j in 1:np)
{
arr.mean[j] <- mean(arr[,j],na.rm=TRUE)
arr.sd[j] <- sd(arr[,j],na.rm=TRUE)
arr.range[j] <- max(arr[,j],na.rm=TRUE) - min(arr[,j],na.rm=TRUE)
}
arr.mean
arr.sd
arr.range
(lm1 <- lm(arr.sd~arr.mean))
(lnlm1 <- lm(log(arr.sd)~log(arr.mean)))
(lm2 <- lm(arr.range~arr.mean))
bitmap(file='test1.png')
plot(arr.mean,arr.sd,main='Standard Deviation-Mean Plot',xlab='mean',ylab='standard deviation')
dev.off()
bitmap(file='test2.png')
plot(arr.mean,arr.range,main='Range-Mean Plot',xlab='mean',ylab='range')
dev.off()
load(file='createtable')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Standard Deviation-Mean Plot',4,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Section',header=TRUE)
a<-table.element(a,'Mean',header=TRUE)
a<-table.element(a,'Standard Deviation',header=TRUE)
a<-table.element(a,'Range',header=TRUE)
a<-table.row.end(a)
for (j in 1:np) {
a<-table.row.start(a)
a<-table.element(a,j,header=TRUE)
a<-table.element(a,arr.mean[j])
a<-table.element(a,arr.sd[j] )
a<-table.element(a,arr.range[j] )
a<-table.row.end(a)
}
a<-table.end(a)
table.save(a,file='mytable.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: S.E.(k) = alpha + beta * Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable1.tab')
a<-table.start()
a<-table.row.start(a)
a<-table.element(a,'Regression: ln S.E.(k) = alpha + beta * ln Mean(k)',2,TRUE)
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'alpha',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[1]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'beta',header=TRUE)
a<-table.element(a,lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'S.D.',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,2])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'T-STAT',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,3])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'p-value',header=TRUE)
a<-table.element(a,summary(lnlm1)$coefficients[2,4])
a<-table.row.end(a)
a<-table.row.start(a)
a<-table.element(a,'Lambda',header=TRUE)
a<-table.element(a,1-lnlm1$coefficients[[2]])
a<-table.row.end(a)
a<-table.end(a)
table.save(a,file='mytable2.tab')